A universal algorithm for transforming chaotic sequences into uniform pseudo-random sequences

Abstract

We present a universal algorithm for transforming chaotic sequences of either chaotic map systems or chaotic differential dynamic systems into uniform pseudo-random sequences. Theoretically，the algorithm is based on bit-operations represented by floating-point algorithm，not aiming at any definite physical chaotic systems. It has been proved that，any real random variable generally has a type of natural tendency of homogenization which exponentially increases bitwise with random variable. As a result，any real chaotic sequence can be completely transformed into the pseudo-random sequence having uniform identical independent distribution. Adopting logistic map，Hénon map and Lorenz system as examples to test the universal validity of the algorithm，respectively，the experiments demonstrate that the algorithm is correct. We can reasonably expect that the universally valid algorithm should become the technological basis of standardized modular design of chaotic pseudo-random sequence generator in hardware implementation.